The relationship between America and Britain is at “the highest level of special”, Donald Trump told a press conference with British Prime Minister Theresa May in the gardens of her country house as part of his two-day UK trip.

The meeting of the two leaders on Friday came hours after the publication of a bombshell newspaper interview that had the potential to disrupt the carefully choreographed visit.

In the interview, Trump berated May and praised Boris Johnson, her political rival who resigned as foreign secretary earlier this week, saying he was a “great” potential prime minister.

“I would have done [Brexit] much differently. I actually told Theresa May how to do it, but she didn’t agree, she didn’t listen to me,” Trump said.

But at the joint question and answer session at Chequers, Trump appeared to U-turn, saying reports he criticised May in the interview were “fake news” and the newspaper didn’t include the “tremendous things” he said about her.

“Once the Brexit process is concluded and perhaps the UK has left the EU, I don’t know what they’re going to do but whatever you do is OK with me, that’s your decision,” Trump told May. “Whatever you do is OK with us, just make sure we can trade together.”

Trump was also positive about a Nato summit earlier in the week which he threw into turmoil by demanding allies reach their commitment to increase spending then told them to eventually double it.

“We were paying 90 per cent of the cost of Nato, and Nato is really there for Europe much more than us … That being said, it is a great unifier. We have 29 countries and there is a lot of love in that room.”

Meanwhile, tens of thousands of protesters were marching through London against Trump.

Some banged on pots and pans, others blew trumpets and many held orange “Stop Trump” balloons.

Campaigners elsewhere in London flew a “Baby Trump” balloon, an act of protest approved by London mayor Sadiq Khan which has proved particularly contentious for Trump and his supporters.

The diaper-clad infant, with a quiff of hair and a mobile phone for tweeting, was the centrepiece of demonstrations protesting Trump’s policies.

“Depicting Trump as a baby is a great way of targeting his fragile ego, and mocking him is our main motivation,” said Matthew Bonner, one of the organisers. “He doesn’t seem to be affected by the moral outrage that comes from his behaviour and his policies. You can’t reason with him but you can ridicule him.”

“As an American, I think it’s great,” said Brett Kirchner, 25, from North Carolina. “Back home in the States, there will be some who are very upset about this protest and who think it’s insulting.”